| Williams.tar | gzipped .tar file of these files |
| README | The README file |
| FrobAlg.py |
Robert's implementation of the Frobenius algorithm for studying a list of Schubert problems.
It is in Python2, runs Singular, and uses the Singular
library schubert.lib.
It reads Schubert problems in a particular format, in schubertprob.txt
(This is formatted by the Python script prettyFormat.py from our
Python library in the
checkerboard game, and the format is explained in FrobAlg.py). For each, it runs the Frobenius
algorithm, determining if it is the full symmetric group, or if it cannot tell.
With suitable modification, it can be used to test other lists of Schubert problems.
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| schubertprob.txt |
This contains the initial list of Schubert problems to be tested.
This was the output of the the Python implementation of Vakil's algorithm,
and is the file from the computations on G49.
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| schubert.lib |
Singular library for computing Schubert problems.
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| Full_Symmetric_Group.txt |
These are the Schubert problems that it found has full symmetric Galois groups.
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| Unknown_Galois_Group.txt |
These are the Schubert problems that is could not tell if they had full symmetric Galois groups.
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| schubert_template.sing |
This is a template file. It should not be altered.
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| SchubertStats.py |
This takes a list of Schubert problems in Unknown_Galois_Group.txt and tries to
compute 50,000 Frobenius elements (this can be changed in the file) for the problem, writing the output to a text file
Schubert_Stats.txt that, for each
Schubert problem in Unknown_Galois_Group.txt contains both a plain text frequency
table of the cycle types found, as well as a formatted LaTeX table.
It uses both schubert.lib and cycle_sample.sing.
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| cycle_sample.sing |
This is a template file. It should not be altered. It could be deleted.
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| Schubert_Stats.txt |
The output from SchubertStats.py.
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| Simplify.py |
This Python 3 script reads Schubert_Stats.txt and writes just the lines with the
Schubert problems and ASCII frequency table to the file Raw_data.txt
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| Raw_data.txt |
The output file from Simplify.py.
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| makeHtml.py |
A Python3 script that reads Raw_data.txt and writes it into a .html file Frobenius_Raw.html.
It needs the file procedures.py.
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| procedures.py |
Procedures for makeHtml.py
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| Frobenius_Raw.html |
The raw data in .html format. This requires .gif files of Young tableaux, which is available
in the .tarball Tableaux.tar.
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| Tableaux.tar |
All the tableaux for Frobenius_Raw.html
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